Germany's leading feminist campaigner and its minister for families, pensioners and women have locked horns over the role of feminism in relationships and the workplace, unsparingly attacking each other's views in a row that has escalated into a nationwide debate.

Alice Schwarzer, considered the country's foremost women's rights campaigner, labelled Kristina Schröder "hopeless" and "incompetent" after Schröder said she thought some of her views were wrong.

Schröder, 33, of the Christian Democratic union, was recruited by Angela Merkel and became the youngest woman ever in a German cabinet. She told Der Spiegel that she could not agree with certain views expressed by Schwarzer, including that "heterosexual sex was hardly possible without the subjugation of women".

Schröder said: "It's absurd to define something that is vital to the survival of humanity as subjugation." She said she was unconvinced by the feminist argument that rejecting heterosexual relationships in favour of homosexuality was a "solution to the disadvantage to women", and blamed boys' underperformance in school on the disproportionate number of female carers and teachers. She also rejected the idea of quotas to improve the standing of women in the workplace.

Schwarzer, 67, author of feminist books such as The Little Difference and its Huge Consequences" and publisher of the feminist magazine Emma, hit back in an open letter, accusing Schröder of using "cheap cliches" about "the most momentous social movement of the 20th century" and said she had not known whether she "should laugh or cry" when she read the interview. She said Schröder was "regurgitating pub talk of the 1970s", but "the pub talk in 2010 is more advanced than you – much more".

Schwarzer added that Schröder, who has been in her post for a year, had the feminist movement to thank for the fact that she was in her job at all. But she said the only noteworthy news to have emerged from her ministry concerned her name change after her recent marriage, and accused her of having done nothing to further the rights of women.

Schwarzer went on to attack Schröder's evaluation that some women were to blame for the fact they earned less than men because they studied the wrong subjects, and her initiative to encourage boys to perform better at school. Schwarzer said such a policy was unnecessary when "out of 185 bosses of Dax companies [those listed on the stock exchange], 181 are male".

The debate quickly drew sharp responses from leading German female politicians. Renate Künast, Green party candidate for Berlin mayor, said she was "flabbergasted" by Schröder's views, which she said were "crude" and "fuddy-duddy".

Manuela Schwesig, deputy chair of the Social Democrats, said Schröder "should be reminded that at the start of the 1970s, women still needed written permission [from their husbands] to take a job. Without the feminist movement, Schröder would not be a minister today."

But Silvana Koch-Mehrin, vice-president of the European parliament and a leading member of the Free Democratic party, the junior coalition partner in the government, said Schröder's views deserved recognition because "we've moved way beyond the classical definition of feminism", to an age when "equal society means that men and women have the chance to follow the same path in life".

Schröder responded to Schwarzer's letter today (Tues), by accusing her of "failing to read the interview properly" and saying it was "a shame" she had "had to deliver such a personal attack on me".